Mathematics · Linear Algebra

Let T: ℝ 4 → ℝ 4 be a linear map with four distinct eigenvalues and satisfying T 4 - 15T 2 + 10T + 24I = 0. Which of the following statements is necessarily true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1There exists a non-zero vector v 1 &in; ℝ 4 such that Tv 1 = 2v 1
2There exists a non-zero vector v 2 &in; ℝ 4 such that Tv 2 = v 2
3For every non-zero vector v &in; ℝ 4 , the set {2v, 3Tv} is linearly independent
4T is a one-to-one function✓

Correct answer

T is a one-to-one function

Save this question and verified answer as a clean study sheet with live clickable link.

👥

Challenge your peer aspirants on WhatsApp or Telegram to solve this question!

Online Test Series

Practice full-length mock tests with real exam timers, instant score analysis, and all-India ranking.

Chapter Practice

Want more practice questions on Linear Algebra?

Solve complete topic-wise tests with detailed solutions on GkGet.

Recommended practice questions in Mathematics · Linear Algebra

Which of the following organizations was instrumental in advocating for the abolition of Sati in India?

Who was the first President of independent India?

Who among the following was the founder of the 'Gadar Party'?

Let T: ℝ 4 &rarr; ℝ 4 be a linear map with four distinct eigenvalues and satisfying T 4 - 15T 2 + 10T + 24I = 0. Which of the following statements is necessarily true?